Wavelets and Multiresolution Processing: Theory and Applications in Signal and Image Analysis

Wavelet transforms and multiresolution analysis have emerged as powerful tools for signal and image processing due to their ability to represent data at multiple scales. Unlike traditional Fourier transforms, wavelets can localize both time and frequency content, making them suitable for applications requiring high spatial and frequency resolution. Conventional signal and image analysis techniques often struggle with noise suppression, edge preservation, and efficient data compression simultaneously. These limitations hinder performance in critical areas such as medical imaging, biometric recognition, and communication systems. This study proposes an enhanced wavelet-based multiresolution framework that integrates Discrete Wavelet Transform (DWT) with adaptive thresholding and region-based fusion techniques. Signals and images are decomposed into subbands, analyzed at various scales, and adaptively filtered to retain important features while minimizing noise. The process is also optimized for computational efficiency using subband prioritization. Experimental analysis on standard signal and image datasets demonstrates significant improvement in denoising performance (PSNR gain of 2–4 dB), edge preservation (SSIM improvement up to 10%), and compression ratio. The method outperforms conventional DWT and Fourier-based approaches, showcasing its potential in real-time and high-resolution applications.